A plane delivers two types of cargo between two destinations. Each crate of cargo I is 2 cubic feet in volume and 73 pounds in weight, and earns $15 in revenue. Each crate of cargo II is 2 cubic feet in volume and 146 pounds in weight, and earns $45 in revenue. The plane has available at most 130 cubic feet and 5,548 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

Answer:38 crates of Cargo I and 19 crates of Cargo II$1425 maximum revenueStep-by-step explanation:First of all, we note that Cargo II crates earn more revenue per cubit foot and more revenue per pound than Cargo I crates, so we want to maximize the shipment of Cargo II.Since 2 crates of Cargo I must be delivered for each crate of Cargo II, it is convenient to bundle them together. Such a bundle will weigh ...   2×73 + 146 = 292 . . . . poundsand will have a volume of ...   2×2 + 1×2 = 6 . . . . ft³Then the number of bundles allowed by the volume limit is ...   (130 ft³)/(6 ft³) = 21  2/3and the number of bundles allowed by the weight limit is ...   (5548 pounds)/(292 pounds) = 19The weight limit is more restrictive, and the number of bundles it allows is an integer, so the load limit will be filled with 19 Cargo II and 38 Cargo I crates. Even though there is extra volume available, the weight limit will not allow any more cargo.The revenue for each bundle is ...   2×$15 +1×$45 = $75so the maximum revenue is 19×$75 = $1425.